Collapse and revival in inter-band oscillations of a two-band Bose-Hubbard model

We study the effect of a many-body interaction on inter-band oscillations in a two-band Bose-Hubbard model with an external Stark force. Weak and strong inter-band oscillations are observed, where the latter arise from a resonant coupling of the bands. These oscillations collapse and revive due to a weak two-body interaction between the atoms. Effective models for oscillations in and out of resonance are introduced that provide predictions for the system's behaviour, particularly for the time scales for the collapse and revival of the resonant inter-band oscillations.